On making optimal transport robust to all outliers

TL;DR

This paper addresses the sensitivity of optimal transport to outliers by proposing a classifier-based detection method that improves robustness in various applications like generative modeling and label propagation.

Contribution

It introduces a novel outlier detection approach using adversarial training to identify and mitigate the influence of outliers in optimal transport problems.

Findings

Successfully detects outliers using classifier-based methods

Reduces outlier influence in transport problems

Improves performance in applications like gradient flows and label propagation

Abstract

Optimal transport (OT) is known to be sensitive against outliers because of its marginal constraints. Outlier robust OT variants have been proposed based on the definition that outliers are samples which are expensive to move. In this paper, we show that this definition is restricted by considering the case where outliers are closer to the target measure than clean samples. We show that outlier robust OT fully transports these outliers leading to poor performances in practice. To tackle these outliers, we propose to detect them by relying on a classifier trained with adversarial training to classify source and target samples. A sample is then considered as an outlier if the prediction from the classifier is different from its assigned label. To decrease the influence of these outliers in the transport problem, we propose to either remove them from the problem or to increase the cost of moving them by using the classifier prediction. We show that we successfully detect these outliers and that they do not influence the transport problem on several experiments such as gradient flows, generative models and label propagation.